Kerry Back
BUSI 721, Fall 2022
JGSB, Rice University
A common belief is that the law of averages will rule in the long run, eliminating risk.
It’s true that the average outcome from a gamble should not be risky in the long run.
But the gain or loss from gambling is average gain per gamble \(\times\) number of gambles.
Based on history, the bet is definitely in our favor. We have much better odds than in a casino.
If we play for a long time, we will almost certainly come out ahead.
But how far ahead is quite uncertain.
nsims = 1000
r = np.random.normal(loc=mn, scale=sd, size=nyears*nsims)
r = r.reshape((nyears, nsims))
comp_ret = np.prod(1+r, axis=0)mean 34.52
std 35.50
min 1.36
10% 7.43
25% 13.07
50% 23.06
75% 43.25
90% 72.34
max 317.80
dtype: float64
Uncertainty about long-run returns \(\Rightarrow\) uncertainty about retirement plans.
We can revisit the retirement plan, but
generate random returns and simulate many lifetimes.